HILLS W: Difference between revisions

Latest revision as of 11:56, 16 October 2024

HILLS_W = [Real]
Default: HILLS_W = $10^{-3}$

Description: HILLS_W specifies the width of the Gaussian hill (in units of the corresponding collective variable) used in metadynamics (in case VASP was compiled with -Dtbdyn).

In metadynamics (MDALGO=11 | 21), the bias potential is given as

{\displaystyle \tilde{V}(t,\xi) = h \sum_{i=1}^{\lfloor t/t_G \rfloor} \exp{\left\{ -\frac{|\xi^{(t)}-\xi^{(i \cdot t_G)}|^2}{2 w^2} \right\}}. }

Thre parameters (HILLS_H, HILLS_W, and HILLS_BIN) must be provided by the user.

The width of the Gaussian hills $w$ (in units of the corresponding collective variable) is set by HILLS_W.

@@ Line 1: / Line 1: @@
-{{TAGDEF|HILLS_W|[Real]|<math>10^{-3}</math>}}
+{{DISPLAYTITLE:HILLS_W}}{{TAGDEF|HILLS_W|[Real]|<math>10^{-3}</math>}}
 Description: {{TAG|HILLS_W}} specifies the width of the Gaussian hill (in units of the corresponding collective variable) used in metadynamics (in case VASP was compiled with [[Precompiler_flags|-Dtbdyn]]).
 ----
-In [[Metadynamics|metadynamics]] ({{TAG|MDALGO}}=11 {{!}} 21), the parameters for the bias potential ({{TAG|HILLS_H}}, {{TAG|HILLS_W}}, and {{TAG|HILLS_BIN}}) must be provided by the user.
+In [[Metadynamics|metadynamics]] ({{TAG|MDALGO}}=11 {{!}} 21), the bias potential is given as
+:<math>
+\tilde{V}(t,\xi) = h \sum_{i=1}^{\lfloor t/t_G \rfloor} \exp{\left\{ -\frac{|\xi^{(t)}-\xi^{(i \cdot t_G)}|^2}{2
+w^2} \right\}}.
+</math>
+Thre parameters ({{TAG|HILLS_H}}, {{TAG|HILLS_W}}, and {{TAG|HILLS_BIN}}) must be provided by the user.
-The width of the Gaussian hills (in units of the corresponding collective variable) used in the [[MDALGO#Metadynamics|metadynamics]] is set by means of the {{TAG|HILLS_W}}-tag.
+The width of the Gaussian hills  <math>w</math> (in units of the corresponding collective variable) is set by {{TAG|HILLS_W}}.
-== Related Tags and Sections ==
+== Related tags and articles ==
+[[:Category:Metadynamics|Metadynamics]],
 {{TAG|HILLS_H}},
 {{TAG|HILLS_BIN}},
+{{FILE|HILLSPOT}},
 {{TAG|MDALGO}}
@@ Line 15: / Line 22: @@
 ----
-[[Category:INCAR]][[Category:Molecular Dynamics]][[Category:Metadynamics]]
+[[Category:INCAR tag]][[Category:Advanced molecular-dynamics sampling]]